Skill points are used to gain Hero skills in many different areas, and you get a few more skill points every time your here gains a new level (see that page for how much).
To assign your skill points you go to Menu -> Hero -> Skills (lower left corner) and distribute your skill points on what you need to boost. It is not possible to boost everything, not even when you have gained all possible points, so you need to select what skills you most need in your current situation. To change your skills you must apply a Second Chance.
For example you can tune your Hero for battle or for training of troops or for producing resources quicker. Since you get more boost when you have all possible levels (or a definitive majority of them) on a particular skill, it is generally a bad idea to spread skill points over as many skills as possible with just a few levels active.
See also list of Skills.